Correlated floating point errors

[James Demmel]

I believe this is just another way of referring to backward error analysis:
A numerical algorithm alg(x), which approximates a mathematical function f(x),
and would equal f(x) were it not for roundoff, is called backward stable if 
alg(x) = f(x+e), where e is small compared to x.
The intermediate results computed inside alg(x) may differ significantly from
their exact counterparts, although the final answer may be fine. This backward
stability property is true of a great many numerical algorithms, such as
matrix computations. This kind of analysis is discussed in many numerical
analysis textbooks.

Jim Demmel
UC Berkeley